The correct options are
A Davaraya I's son Devaraya II became the king because of the hereditary reasons.
B Saluva Narasimha usurped the throne from the last ruler of the Sangama dynasty.
D The three ways in which one could rule the Vijayanagara kingdom was either by inheritance, usurping or by a regent.
After Bukka Raya died. His son, Harihara II, became the emperor. Then his son, Devaraya I and later his son Devaraya II. Saluva Narasimha usurped the throne from the last ruler of the Sangama dynasty. Sadashiva Raya was the emperor, and his regent was Rama Raya.